The mean square error of a randomly discounted sequence of uncertain payments

Expressions are developed for the mean square deviation between a discounted sequence of uncertain payments and the estimated present value. These formulas incorporate random variation from four sources: (1) from the fact that expected values of individual payments are estimated, (2) from the fact that future discount factors are estimated, (3) random variation in the events that give rise to future payments, and (4) random variation in future discount rates. The results extend and encompass existing expressions based on the assumed constancy of one or more of the random vectors.